Self-assembly of correlated (Ti, V)O2 superlattices with tunable lamella periods by kinetically enhanced spinodal decomposition

Spinodal decomposition, the spontaneous phase separation process of periodic lamellae at the nanometer scale, of correlated oxide ((Ti, V)O2) systems offers a sophisticated route to achieve a new class of mesoscale structures in the form of self-assembled superlattices for possible applications using steep metal–insulator transitions. Here, we achieve the tunable self-assembly of (Ti, V)O2 superlattices with steep transitions (ΔTMI < 5 K) by spinodal decomposition with accurate control of the growth parameters without conventional layer-by-layer growth. Abrupt compositional modulation with alternating Ti-rich and V-rich layers spontaneously occurs along the growth direction because in-plane lattice mismatch is smaller in this direction than in other directions. An increase in the film growth rate thickens periodic alternating lamellae; the phase separation can be kinetically enhanced by adatom impingement during two-dimensional growth, demonstrating that the interplay between mass transport and uphill diffusion yields highly periodic (Ti, V)O2 superlattices with tunable lamellar periods. Our results for creating correlated (Ti, V)O2 oxide superlattices provide a new bottom-up strategy to design rutile oxide tunable nanostructures and present opportunities to design new material platforms for electronic and photonic applications with correlated oxide systems. Mixtures of metal oxides can now be easily separated into nanoscale-thin layers known as superlattices with intriguing switching capabilities. Theory predicts that superlattices made from alternating vanadium and titanium oxide layers may show temperature-dependent transitions from electrically conductive to insulating states close to room temperature. Junwoo Son and Si-Young Choi from the Pohang University of Science and Technology in South Korea and co-workers have exploited a mechanism similar to the rapid separation of oil/water mixtures to self-assemble these superlattices in just a few minutes. Using pulsed lasers, the team directed vanadium and titanium ions toward a target held close to 400 °C. Under optimal conditions, the metal ions diffused into separate phases and self-assembled into a superlattice. The superlattices thicknesses could be specifically tuned to between 5 and 15 nanometers by adjusting laser pulse frequencies. Spinodal decomposition, spontaneous phase separation process for periodic lamellae at the nanometer scale, of correlated oxides (Ti, V)O2 systems offers a sophisticated route to achieve new class of mesoscale structure in the form of self-assembled superlattices. Here, we achieve the tunable self-assembly of (Ti, V)O2 superlattices with steep metal-insulator transition (ΔTMI < 5 K) by spinodal decomposition with accurate control of growth parameters. Increase in a film growth rate thickens a lamellae period; the phase separation were kinetically enhanced by adatom impingement during two-dimensional growth, demonstrating that interplay between mass transport and uphill diffusion yields highly periodic (Ti, V)O2 superlattices.


Introduction
Superlattices, structures with periodic blocks on the nanometer scale, have realized unique properties unachievable with the use of a single layer via structural and electronic confinement effects [1][2][3][4] . While superlattices can be artificially fabricated using film growth with layer-bylayer control, self-assembly by thermodynamically driven phase separation provides a straightforward and simple route to naturally form superlattices 5,6 , which leads to distinct physical properties (e.g., superconductivity 7 , multiferroicity 8,9 , and high ionic conductivity 10,11 ) unobtainable in single-phase materials. When the materials are largely immiscible, the reaction-controlled phenomena involving nucleation and growth give rise to the phase separation process, and therefore, a large number of randomly distributed nuclei grow into a type of irregular nanodot-embedded nanocomposite (0D) 7 or nanopillarembedded nanocomposite (1D) [8][9][10][11] . Unlike nucleation and growth, spinodal decomposition is a unique thermodynamic, diffusion-controlled phenomenon that leads to spontaneous formation of multiple phases from a uniform mixture, and the process occurs due to longrange spatial and periodic compositional modulations on the nanometer scale. This unique feature of spinodal decomposition has been exploited to obtain highly periodic nanostructures, e.g., self-assembled two-dimensional superlattices in III-V semiconductors [12][13][14] , metal alloys 15,16 , and transition metal oxides [17][18][19] systems.
Since TiO 2 /VO 2 superlattices are uniquely composed of 3d 1 -correlated functional materials coupled with isostructural 3d 0 insulators, they are predicted to have electrical and optical properties that can be tuned by external stimuli to provide a new platform for thin-film devices (i.e., half-metallic VO 2 slabs 20 and tunable metamaterials 19,21 ). Layer-by-layer growth of TiO 2 /VO 2 superlattices has been previously attempted, but the methods allowed excessive Ti diffusion into VO 2 layers and the formation of TiO 2 anatase polymorphs; therefore, these methods did not guarantee tunable and steep metal-insulator (MI) transition behavior in the superlattice 21 .
The TiO 2 /VO 2 system has been recently demonstrated in the bulk as an example of spinodal decomposition in the rutile oxide family. Spinodal decomposition occurs below 830 K if atomic diffusion is thermally activated 22 . This spinodal decomposition strongly depends on the crystallographic anisotropy that emerges from the anisotropic lattice parameters of a rutile oxide with tetragonal symmetry; compositional modulation of the lamellar structure preferentially appears normal to the c-axis rather than the a-axis because the lattice mismatch between TiO 2 and VO 2 is smaller along the a-axis (~1.5 %) than the c-axis (~3.7 %). In short, the formation of periodic Ti-rich and V-rich lamellae normal to the a-axis is the only option to minimize the elastic strain energy at the interfaces between two rutile phases, resulting in the generation of well-ordered superlattices 22,23 .
Recently, for the application of tunable metamaterials, spinodal-decomposed (Ti, V)O 2 nanocomposite layers have been achieved by post-annealing 19 , but these layers have an inferior structural order that was damaged by significant numbers of stacking faults and dislocations and by large variation among the lamellar periods; all of these traits can degrade the desirable properties of these nanocomposites. Furthermore, despite the potential importance of the accurate control of mesoscale dimensions in the (Ti, V)O 2 superlattices, there has been no promising method to tune the periodicity of a naturally assembled high-quality superlattice film by spinodal decomposition.
Here, we provide the first demonstration of selfassembled high-quality superlattices in (Ti, V)O 2 thin films from homogeneously mixed targets (Ti:V = x:1−x, x = 0.4, 0.5, and 0.55) and the precise control of lamellar periods (Λ) by adjusting the growth parameters of pulsed laser deposition (PLD) (Fig. 1). Unlike artificial superlattices that are assembled using layer-by-layer growth 21,24 , alternating Ti-rich and V-rich layers with accurate thicknesses and atomically abrupt interfaces spontaneously formed by kinetically enhanced spinodal decomposition even without a post-annealing step. These traits yield abrupt MI transition characteristics (ΔT MI < 5 K) with narrow hysteresis in superlattices~50-nm thick. Lamellar periods induced by spinodal decomposition are highly tunable from 5.47 to 16.53 nm by adjusting the laser pulse frequency f to control the growth rate. This accurate control of spontaneous phase separation without post-annealing is attributed to the mass transport promoted by ion impingement during PLD growth and the consequent significant acceleration of uphill diffusion for spinodal decomposition. Therefore, our demonstration of producing self-assembled superlattices paves the way to design new superlattices with functionalities in nanoarchitectured materials that have strong correlations.

Results and discussion
The growth of self-assembled high-quality (Ti, V)O 2 superlattices Epitaxial Ti-rich/V-rich (Ti, V)O 2 superlattices were grown on (001) TiO 2 substrates using a KrF pulsed laser to ablate a homogeneously mixed target (Fig. 1). Depending on the growth temperature T g , the degree of the phase separation was significantly modulated at a constant laser pulse frequency (f = 7 Hz), target composition (Ti:V = 0.5:0.5), and oxygen partial pressure (10 mTorr). X-ray diffraction (XRD) results (Fig. 2a) indicate that films grown at low T g (~200°C) show a single (002) Bragg peak with thickness fringes around the (002) peak, which indicates a flat and homogeneous (Ti, V)O 2 solid solution. This result suggests that phase separation is kinetically suppressed at low T g . The periods (Λ) and thicknesses of each layer could be accurately controlled by adjusting the growth parameters (growth temperature T g , laser pulse frequency f, and target composition x) Figure 2a, interestingly, shows that the T g of 420°C results in distinct satellite peaks developing up to the fourth order, indicating that spontaneous phase separation occurs because atomic diffusion is thermally activated 19,22 . These higher-order satellite peaks never appear when the composition gradually changes along the interfaces of the superlattices, as reported in recent studies on (Ti, V)O 2 superlattices 19,21,24 . Therefore, the appearance of these high-order peaks at 420°C suggests that the interfaces are sharp and that the superlattices are of high quality with composition modulations similar to a square wave along the c-axis. As T g is further increased up to 450°C, the satellite peaks and thickness fringes broaden and become unclear due to excess atomic diffusion from thermal energy. These characteristics are similar to those of randomly separated (Ti, V)O 2 thin films with inferior structural quality 19 . Based on our structural analysis, we infer that to obtain high-quality superlattices with abrupt interfaces and regular periodicity by spinodal decomposition, T g must be precisely controlled between 400 and 450°C.
From the position of the Bragg peaks, the estimated average out-of-plane lattice parameters were 2.924 Å in solid-solution films and 2.917 Å in superlattice films grown at the optimized T g~4 20°C. This result suggests that the out-of-plane lattice parameter of the V-rich layer shrinks by coherently adhering to the Ti-rich layer that has a larger in-plane lattice parameter 22,24 . In addition, ω scans of the superlattices and solid solutions show similar full-width at half-maximum values; this similarity means that the two phases have a similar crystal quality (Fig. S1). Compositional modulation occurs selectively along the caxis because the in-plane lattice mismatch between the Vrich and Ti-rich layers is smaller than the out-of-plane lattice mismatch. Thus, the preferred modulation direction is determined to minimize the strain energy at the interface between the two phases and yield a well-ordered superlattice 22 . Unlike spinodal decomposition of bulk (Ti, V)O 2 with a random distribution of periodicity (10-50 nm) and structural imperfections (e.g., incomplete stacking sequences or misfit dislocations) 22,23 , the periodicity and thickness of each layer could be accurately controlled during PLD growth, resulting in better structural quality with coherent interfaces 19,22,23 .
This method of assembling high-quality superlattices by spinodal decomposition during PLD growth is rapid; the process requires only a few minutes, unlike previous reports 19,22,23 on spinodal decomposition of (Ti, V)O 2 by post-annealing, which required at least several hours. We post-annealed our solid-solution Ti 0.5 V 0.5 O 2 films at 420°C for more than 7 h, which is much longer than the growth time (a few minutes), but no satellite peak was observed (Fig. S2). Therefore, the results indicate that the periodic lamellar growth by PLD is caused by adatom kinetics during the PLD process rather than the thermodynamic stability.
To further understand how growth parameters influence the formation of well-ordered superlattices during PLD growth, f and target compositions were varied at the optimized T g (~420°C) (Fig. 2b-d). Almost all of these samples showed superlattice satellite peaks regardless of f. The exceptions were the samples grown from Ti:V = 0.55:0.45 target at f = 1 or 2 Hz (Fig. S3). However, as f was increased, the distance between adjacent satellite peaks was tuned. From the distance between adjacent satellite peaks, the thickness Λ [nm] of one period in the superlattices could be calculated as where m is the order of the satellite peak, λ is the X-ray wavelength, θ m is the angle of the m th order satellite peak, and θ B is the average Bragg angle for the superlattice.  (Table S1). It should be noted that the samples grown from the Ti:V = 0.4:0.6 and Ti:V = 0.5:0.5 targets exhibit more of a tendency to undergo phase separation than those grown from Ti:V = 0.55:0.45, probably because both target compositions are in the range of the spinodal regions based on the TiO 2 -VO 2 phase diagram 22 .
To verify the epitaxial relationship in the self-assembled superlattices, XRD reciprocal space mapping (RSM) around the (112) TiO 2 Bragg peak of the self-assembled Ti 0.4 V 0.6 O 2 superlattice grown at 420°C was performed below (~288 K) and above (~373 K) the MI transition temperature T MI of VO 2 (Fig. 2e). The average c-axis lattice parameter of the superlattice decreased slightly from 2.903 to 2.900 Å as T g increased; this reduction in the lattice parameter is evidence of a structural phase transition (monoclinic to rutile) of the phase-separated V- 22,24 . The second-order satellite peaks were clearly observed with the main Bragg peak of the superlattices along the q z (out-of-plane) directions, which agrees with the results of the XRD θ-2θ scan. The substrate and superlattice peaks (i.e., Bragg peak and satellite peaks) had identical q x values, which means that entire layers in the~50-nm-thick superlattices are coherently strained by the rigid TiO 2 substrates despite the large lattice mismatch between the V-rich phase and the Ti-rich phase (or TiO 2 substrate).
Atomically ordered superlattices were confirmed by an atom-scale STEM analysis. As shown in Fig. 3a, V-rich layers with bright contrast alternate with Ti-rich layers, with abrupt interfaces on the (001) TiO 2 substrate. Although Ti and V have similar atomic numbers, the contrast between the alternating layers was significant in the high angle annular dark field (HAADF) images, probably as a result of strain effects 25,26 , which causes more electron scattering in the less symmetric monoclinic V-rich layer than in the rutile Ti-rich layer. Along with the contrast in the HAADF images, a difference in the crystal symmetry was also observed between the lamellar structures. The Ti-rich layer is a high-symmetry rutile structure, but the FFT image of the V-rich layer shows diffraction spots of superstructures (right side of Fig. 3a, yellow circles); these spots indicate monoclinic structures due to the formation of the V 4+ ion dimer 19,22,23 . Moreover, our self-assembled superlattices showed no defects at the interface, meaning that the alternating layers were fully strained with perfectly coherent interfaces, as predicted by the RSM analysis. The variation in the c-lattice and a-axis lattice parameters in each layer, Δc/c and Δa/a, was extracted using GPA (geometric phase analysis, HREM Research Inc.), as shown in Fig. S4. The Δc/c in the V-rich layer is approximately −0.03, which concurs with previous reports that the parameter is 3.0% larger in the Ti-rich layer than in the V-rich layer in phase-separated (Ti, V)O 2 created using spinodal decomposition 22,23 . On the other hand, the Δa/a values of the in-plane lattice parameter of both Ti-rich and V-rich layers were coherently constrained by interactions with the rigid TiO 2 substrates in our superlattices (Fig. S4); as a result, tension could be significant only in the V-rich layers with negligible strain in the Ti-rich layers along the in-plane direction. With an assumption of Vegard's law 27 , the Δc/c in the V-rich layer, V 0.9 Ti 0.1 O 2 , is expected to be approximately −0.027, and therefore, the actual strain in the V-rich layer is approximately −0.3% (compressive) along the out-of-plane direction. For better accuracy of the strain analysis, we measured the Δc/c by using off-axis in-line holography TEM (Fig. S5) 28,29 , wherein a much wider field of view can be used compared to the GPA method and the rigid TiO 2 can be used as a reference guaranteeing better accuracy. The Δc/c values in the V-rich layers are approximately −0.023 except for the first V-rich layer having a Δc/c value of approximately −0.019. Therefore, the strain in the V-rich layers is approximately +0.4% (tensile) along the out-of-plane direction, and the first V-rich layer exhibits a stronger tensile strain of~0.8%. This structural modulation in our superlattices is inconsistent with previous reports on phase-separated bulk (Ti, V)O 2 with alternately stacked compressive Ti-rich and tensile V-rich layers 22,23 .
Compositional modulations with sharp interfaces between alternating lamellae can be visualized directly by detecting V L-edges (513−528 eV) and Ti L-edges (455 −468 eV) using electron energy loss spectroscopy (EELS) and a corrected electron probe of 0.8 Å on a selected area (Fig. 3b). In the EELS spectra of the Ti-rich layer, the dominant peaks occur at 457.7 eV (L 3 -edge) and 463.2 eV (L 2 -edge); in the EELS spectra of the V-rich layer, the dominant peaks occur at 518.4 eV (L 3 -edge) and 524.9 eV (L 2 -edge). The 5.5 eV L 2,3 -edge splitting in the Ti-rich layer and 6.5 eV L 2,3 -edge in the V-rich layer are similar to those in previous XAS or EELS studies on rutile TiO 2 and monoclinic VO 2 systems [30][31][32][33] . As shown on the right side of Fig. 3b, the energy difference between t 2g and e g in the Ti L 3 -edge in the Ti-rich lamella is found to be~2.1 eV 34 , and the L 3 /L 2 ratio in the V L-edges is comparable to 1 35 . Both of these results imply that the valence states of Ti and V are likely to be +4. Therefore, Ti and V maintain their original valence states, and thus, there should be almost no atomic scale defects (i.e., oxygen vacancies) decreasing the valence states of Ti and V. The weak signals of the Ti L 2,3 -edges in the V-rich layers and the weak signals of the V L 2,3 -edges in the Ti-rich layers indicate that the phases are only slightly soluble in each other, so the local composition profile can be estimated from the relative intensity of the dominant and minor EELS signals of each layer. The EELS spectra suggest that the V-rich layers are likely to be Ti 0.1 V 0.9 O 2 and that the Ti-rich layers are likely to be Ti 0.6 V 0.4 O 2 . These compositions match well with those of the separated phases in bulk polycrystalline or single-crystal Ti 0.4 V 0.6 O 2 at T g~4 20°C by spinodal decomposition 22,23 . Λ, i.e., the sum of the images of the monoclinic V-rich layer (red square) and the rutile Ti-rich layer (blue square). The FFT of the Ti-rich layers shows high-symmetry rutile structures, whereas the V-rich layers show diffraction spots of superstructures, which indicate the formation of monoclinic structures due to the formation of V 4+ ion dimers. b EELS spectra mapping along the growth direction (yellow arrow) and the corresponding EELS spectra of the Ti-rich layer (orange), the V-rich layer (green), and TiO 2 substrate (black). Ti/V ratio of compositional modulation as a function of thickness estimated from the EELS spectra V-rich layer and Ti-rich layer thickness, observed in the STEM image was estimated to be~8.9 nm, which is comparable to the value of~8.6 nm estimated using the satellite peak of the XRD pattern.

Abrupt MI transition in self-assembled (Ti, V)O 2 superlattices
The degree of phase separation in our periodic (Ti, V) O 2 superlattices obtained by spinodal decomposition was further explored using temperature-dependent sheet resistance R S measurements (Fig. 4). Indeed, electrical transport in (Ti, V)O 2 superlattices was highly correlated with the self-assembly of (Ti, V)O 2 by spinodal decomposition. In the solid solution of Ti 0.5 V 0.5 O 2 grown at 200°C, which is kinetically suppressed due to insufficient atomic diffusion, the insulating state was maintained without an MI transition. However, as T g increased, sufficient thermal energy was supplied to drive the thermodynamically stable phase separation of Ti-rich and V-rich phases; thus, an abrupt MI transition induced by the Vrich phase appeared at T MI with an orders of magnitude change in the R S of the superlattices grown at the optimized T g~4 20°C for phase separation (Fig. 4a). Thus, phase separation in the superlattices is required for the MI transition in electrical transport.
Furthermore, since the XRD results suggest that the growth rate affected the degree of phase separation of the superlattice, the change in the MI transition was investigated in the self-assembled superlattices grown under different laser frequencies (1 ≤ f ≤ 7 Hz) with different Ti mole fractions (x = 0.4, 0.5, and 0.55) of targets at T g4 20°C (Fig. 4b-d). The insulating phase without an MI transition appeared only in the Ti 0.55 V 0.45 O 2 samples grown at f = 1 or 2 Hz; this result is consistent with the absence of satellite peaks in the XRD patterns. In all other samples, the MI transition occurred, but the abrupt MI transition tended to be suppressed as f decreased, which indicated that the growth rates substantially affect the steepness of the MI transition in the self-assembled (Ti, V)O 2 superlattices.
The increase in the thickness of the V-rich lamellae with an increase in f suggests that increasing the thickness of the V-rich layers induced by spinodal decomposition favors an increase in the steepness of the MI transition. To quantify how the thickness of the V-rich phase affected electrical transport, the nominal thickness of the V-rich layer was quantitatively calculated based on the superlattice periods and the lever rule (Table S2). Universally, the abrupt transition was suppressed when the calculated thickness of the phase-separated V-rich layer was less than a critical thickness of~3 nm due to the slight interdiffusion between Ti and V atoms along both layers, which was also previously observed in ((TiO 2 ) m /(VO 2 ) n ) r superlattices 24 and ultrathin epitaxial VO 2 thin films 25,36 on a (001) TiO 2 substrate.
Interestingly, the MI transition of self-assembled superlattices is steeper (ΔT MI < 5 K) than that of the ((TiO 2 ) m /(VO 2 ) n ) r superlattices 24 or Ti-doped VO 2 epitaxial thin films 37 , and this difference is ascribed to the chemically abrupt interface between the V-rich and Tirich phases in our superlattices. Along with the steep MI transition in our self-assembled superlattices, the T MI of the superlattices (313-307 K) was consistently~30 K less than that in bulk VO 2 regardless of the average compositions of the superlattices. Because Ti doping in VO 2 is known to increase T MI

22
, Ti doping is unlikely to be the origin of the reduced T MI in our case. Rather than doping issues, the homogeneously accumulated tensile strain in the superlattice film mainly contributes to the reduction in T MI because both V-rich and Ti-rich lamellae formed on the rigid TiO 2 substrate, as demonstrated in RSM (Fig. 2e) 38 .
We found another interesting issue in our superlattice VO 2 film. Single VO 2 (or V-rich) epitaxial films are usually relaxed on a TiO 2 substrate due to the high tensile strain when the films are thicker than 15 nm (i.e., the critical thickness for a strained VO 2 single layer), which is accompanied by the line cracks 25,38-41 that substantially Although thick VO 2 films that retain the abrupt MI transition can be achieved on a (001) TiO 2 substrate by inserting a buffer layer (SnO 2 ), the films are relaxed in a different way by texturing columnar VO 2 structures without any line cracks 42 . Therefore, obtaining crack-free and strained films thicker than 15 nm with abrupt MI transitions has been a difficult challenge. Surprisingly, our 50-nm-thick self-assembled superlattices are fully strained and exhibit no cracks (Fig. S1), which are attributed to the fully strained ultrathin V-rich layers sandwiched by Ti-rich bottom and top layers; this crackfree structure leads to single-step steep temperaturedependent MIT with a decreased MI transition temperature (T MI ) (Fig. 4) for electrical transport, which cannot be achieved in single V-rich epitaxial films 39 and even in (TiO 2 ) m /(VO 2 ) n superlattices obtained by layerby-layer growth 43 .

Mechanism of the formation of self-assembled (Ti, V)O 2 superlattices during growth
To elucidate the formation mechanisms of the selfassembled superlattices during PLD growth in (Ti, V)O 2 systems, Λ was plotted as a function of the growth rate, which is controlled by f, for superlattices with different Ti/V ratios (Fig. 5a). In all cases, Λ increased linearly as the growth rate increased, regardless of the Ti/V ratio, indicating that sufficient energy for atomic diffusion is available with the increasing growth rate 9,44,45 . If spinodal decomposition is determined by the thermal uphill diffusion as a basic process leading to phase separation, Λ should decrease as the growth rate increases based on conventional spinodal decomposition 45 ; this is contrary to the observations; thus, in our case, some factor other than thermal diffusion determines Λ 45 .
During film growth, mass transport by ion impingement, as well as uphill thermal diffusion for spinodal decomposition, has a strong contribution to Λ. Ion impingement during PLD growth lowers the activation energy for mass transport of spinodal decomposition according to the following equation 15,17 : where Q * = Q−αI, D* represents the increased diffusion coefficient, D 0 is the initial diffusivity, Q is the activation energy without ion impingement, 0 < α < 1 is a constant and I is the energy flux from ion impingement. Therefore, the increased energy flux with increasing laser pulse frequency would reduce Q * for uphill diffusion; the reduction in Q * causes an increase in the diffusion coefficient and accordingly increases the period of the superlattices. The increased mass transport (i.e., diffusivity) by ion impingement from the PLD plume seems to reduce the activation energy for atomic diffusion and thus should be a more dominant mechanism than thermal diffusion in our case. Indeed, estimates of Q * for spontaneous formation of our superlattices were in the range from 0.436 to 0.574 eV, which are much smaller than that reported for Ti diffusion in a rutile TiO 2 system (1.0 ≤ Q * ≤ 1.2 eV) 46,47 (Fig. 5b). Furthermore, the estimated Q * decreased as f (i.e., the growth rate) increased (e.g., 0.574 ± 0.011 eV at f = 3 Hz to 0.436 ± 0.078 eV at f = 7 Hz); this change may occur because the vanadium and Change in periods Λ with growth rate in self-assembled Ti x V 1-x O 2 (x = 0.4, 0.5, and 0.55) superlattices. The growth rate was calculated by dividing the total thickness by the growth time. Λ increased as the growth rate increased. b Arrhenius plot of Λ in Ti 0.5 V 0.5 O 2 superlattices with different laser frequencies f. The activation energy decreased from 0.574 ± 0.011 eV at f = 3 Hz to 0.436 ± 0.078 eV at f = 7 Hz; the change is attributed to a considerable increase in mass transport during impingement by V and Ti ions generated by the excimer laser titanium ions formed by the focused excimer laser considerably increased mass transport during ion impingement 48 . Because thin-film epitaxy is a nonequilibrium process governed by a competition between kinetics and thermodynamics, the acceleration of kinetics by ion impingement enables the formation of spontaneously ordered superlattices without long thermal annealing times; this process cannot be achieved by bulk synthesis under an equilibrium process 17,18 .

Conclusions
In summary, we have successfully demonstrated the creation of high-quality self-assembled (001) Ti x V 1-x O 2 (x = 0.4, 0.5, and 0.55) superlattices with tunable periods by kinetically enhanced spinodal decomposition driven by ion-impingement effects during PLD growth. The superlattice period Λ could be accurately and uniformly controlled from 5.47 to 16.53 nm by varying the laser pulse frequency (1 ≤ f ≤ 7 Hz) at the optimized growth temperature (420°C) with three compositions of targets (x = 0.4, 0.5, and 0.55). Λ increased as f (i.e., growth rate) increased; as a result, the MI transition in the superlattices became steeper. The increased mass transport due to ionimpingement effects reduces the activation energy and increases the diffusion coefficients for spinodal decomposition, so highly periodic (Ti, V)O 2 superlattices with tunable lamella periods can be produced in a relatively short time. These results provide a new strategy for bottom-up design of correlated (Ti, V)O 2 oxide superlattices as a new platform material for electronic and photonic applications.

Materials and methods
The growth of self-assembled heteroepitaxial Ti x V 1-x O 2 (x = 0.4, 0.5, and 0.55) superlattices Epitaxial Ti-rich/V-rich (Ti, V)O 2 superlattices with thicknesses of 44-55 nm were grown on (001) TiO 2 substrates using PLD (Coherent Compex Pro 102F) to ablate homogeneously mixed targets. The stoichiometric targets for PLD growth were prepared by sintering drymilled stoichiometric powders of V 2 O 5 (99.99%, Sigma-Aldrich) and TiO 2 (99.95%, Sigma-Aldrich) at 600°C for 6 h. The compositions of these targets (x = 0.4, 0.5, and 0.55) were analyzed by energy-dispersive X-ray spectroscopy using high-resolution FE-SEM (JSM 7401F, JEOL). The (001) TiO 2 single crystal substrates (Shinkosha) were loaded onto the substrate holder in the PLD chamber, which was then evacuated to a base pressure of~5 × 10 −7 Torr. Then, the rotating targets were ablated by focusing a KrF excimer laser (λ = 248 nm) with a fluence of 1 J/cm 2 and various pulse repetition rates (1 ≤ f ≤ 7 Hz). The growth was performed at a fixed oxygen partial pressure of~10 mTorr with various substrate temperatures of 200 ≤ T g ≤ 450°C, which were accurately controlled by placing a thermocouple in the cavity of the substrate holder. After growth, the samples were cooled to room temperature at a rate of 20°C/min.

Materials characterization
For structural characterization, high-resolution X-ray scattering measurements (symmetric 2θ-ω scan and asymmetric RSM) were conducted using synchrotron radiation (λ = 0.15401 nm, energy = 10 keV) at the 3D XRD beamline of the Pohang Light Source-II. Out-ofplane and in-plane lattice parameters were also measured using an HRXRD (Discover 8, Bruker).
The STEM sample was prepared by mechanically grinding samples to a thickness of~70 μm, dimpling them to a thickness of~10 μm, and then ion milling the samples using Ar + . HAADF-STEM analysis was performed using a STEM (JEM-2100F, JEOL) at 120 kV equipped with an aberration corrector (CEOS GmbH). For chemical analysis, an EELS line scan was performed using an EEL spectrometer (GIF Quantum spectrometer, Gatan) with a dispersion range of 0.05 eV and dual EELS mode for the Ti L-and V L-edges. The collection semiangle from the HAADF detector under 120 kV ranged from 50 to 160 mrad, and the convergence semiangle for EELS acquisition was 15 mrad. All HAADF-STEM images were bandpass filtered to reduce background noise (HREM Research Inc.).
Electronic characterization for sheet resistance versus temperature was performed in the van der Pauw geometry during heating and cooling from 280 to 350 K with square samples (5 × 5 mm) and indium ohmic contacts (<1 × 1 mm) in the sample corners. The four-terminal resistances were measured with a 1 μA current.
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